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stat100_midterm_spring2010_solutions - Initials Statistics...

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Initials: Statistics 100 Spring 2010 Midterm Examination Solutions Monday, 8 March 2010 Name: Section TF/day and time: Put your name on the first page and your initials at the top of each page. This is an open book, open notes exam. You may refer to your problems sets and any material distributed in the course, but all your work must be your own. The exam has 4 problems (each with several parts) and 9 pages. Please check your exam to insure it is complete. Tables of the Normal distribution will be distributed during the exam. You may also use the tables in the back of your text. Some questions are more difficult than others, and the questions may not appear in order of difficulty. Do not spend too much time on any one question; if you find a problem difficult, try another part of the problem or another problem. Some parts of problems ask more than one question. Be sure to read the questions carefully. Some parts of a question may require the answer to an earlier part. If you cannot solve the earlier part, you can still receive partial credit for the later parts: make up a reasonable answer for the earlier part and use that in solving the later parts. You may use (in fact, you are strongly advised to use) a pocket calculator to do the calculations required on the exam. You may not use your cell phone as a calculator or your laptop. Show your work and explain your reasoning; the final answer is not as important as the process by which you arrived at that answer. We can more easily give you partial credit if you have explained your steps. Problem Scoring Problem Point Value Problem Grade 1 22 2 20 3 31 4 27 Total 100 Page 1 of 9
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Initials: 1. (22 total points) Summary statistics; the Normal distribution (a) (4 points) The histogram below shows the distribution of the length at birth (in centimeters) of 100 low birth weight babies born at the Brigham and Women’s Hospital in Boston. Is the distribution skewed right, skewed left or symmetric? You need not justify your answer. Skewed left. 0 0 .1 .1 .2 .2 .3 .3 Fraction Fraction 20 20 25 25 30 30 35 35 40 40 length length (b) (4 points) The mean length of the 100 babies in part (a) is 36.82 cm. Pick the value that is the median and justify your answer: (1) 42 cm (2) 38 cm (3) 30 cm The median is 38cm. The median is larger than the mean in left-skewed data, so 30 is too small, and the histogram shows that 42 is too large to be the median.
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